Extension Theorems for Spaces Arising from Approximation by Translates of a Basic Function Original Research Article

We establish extension theorems for functions in spaces which arise naturally in studying interpolation by radial basic functions. These spaces are akin in some way to the non-integer-valued Sobolev spaces, although they are considerably more general. Such extensions allow us to establish local error estimates in a way which we make precise in the introductory section of our paper. There are many other applications of these fundamental results, including improved Lp error estimates for interpolation by shifts of a single basic function, but these applications have been left to a later paper.